Naphthalene, commonly found in moth balls, is composed of 93.7% carbon and 6.3% hydrogen. The molar mass of naphthalene is 128 g/mol. Determine the empirical and molecular formulas of naphthalene.

Molecular formula naphthalene → C₁₀H₈

Empirical formula naphthalene → C₅H₄

Explanation:

Centesimal composition means that in 100 g of compound we have x g of the element. Therefore in 100 g of naphthalene we have:

93.7 g of C

6.3 g of H

Let's make a rule of three:

In 100 g of naphthalene we have 93.7 g of C  and 6.3 g of H

In 128 g of naphthalene we would have:

128 . 93.7 / 100 = 120 g of C

128.  6.3 / 100 = 8 g of H

We convert the mass to moles, by molar mass:

120 g . 1mol / 12 g = 10 moles C

8 g . 1mol/ 1g = 8 moles H

Molecular formula naphthalene → C₁₀H₈

Empirical formula naphthalene → C₅H₄

(The sub-index of each element is divided by the largest possible number)

The empirical formula is C5H4

The molecular formula is C10H8

Explanation:

Step 1: Data given

Suppose the mass = 100 grams

Naphthalene contains:

93.7 % C = 93.7 grams

6.3 % H = 6.3 grams

atomic mass of C = 12.01 g/mol

atomic mass of H = 1.01 g/mol

Molar mass of naphthalene = 128 g/mol

Step 2: Calculate moles

Moles = mass / molar mass

Moles C = 93.7 grams / 12.01 g/mol

Moles C = 7.80 moles

Moles H = 6.3 grams / 1.01 g/mol

Moles H = 6.24 moles

Step 3: Calculate mol ratio

We divide by the smallest amount of moles

Moles C: 7.80 moles / 6.24 moles

Moles C: 1.25

Moles H: 6.24 moles / 6.24 moles

Moles H: 1

The empirical formula is C5H4

The molecular weight is 64.09 g/mol

128 g/mol / 64.09 g/mol = 2

We have to multiply the empirical formula by 2

2*(C5H4) = C10H8

The molecular formula is C10H8